Preface: The exploration on which this work rests was begun towards the end of 1959. The subsequent record of it owes much, in its early stages, to the friendship and encouragement of Lord Russell, who was one of the few men at the beginning who could see a value in what I proposed to do. It owes equally, at a later stage, to the generous help of Dr J C P Miller, Fellow of University College and Lecturer in Mathematics in the University of Cambridge, who not only read the successive sets of printer's proofs, but also acted as an ever-available mentor and guide, and made many suggestions to improve the style and accuracy of both text and context. In 1963 I accepted an invitation of Mr H G Frost, Staff Lecturer in Physical Sciences in the Department of Extra-mural Studies in the University of London, to give a course of lectures on the mathematics of logic. The course was later extended and repeated annually at the Institute of Computer Science in Gordon Square, and from it sprang some of the context in the notes and appendices of this essay. I was also enabled, through the help of successive classes of pupils, to extend and sharpen the text. Others helped, but cannot, alas, all be mentioned. Of these the publishers (including their readers and their technical artist) were particularly cooperative, as were the printers, and, before this, Mrs Peter Bragg undertook the exacting task of preparing a typescript. Finally I should mention the fact that an original impetus to the work came from Mr I V Idelson, General Manager of Simon-MEL Distribution Engineering, the techniques here recorded being first developed not in respect of questions cf logic, but in response to certain unsolved problems in engineering.

Machines and Biology have been, since antiquity, closely related. From the zoological figures present in astronomical simulacra, through renaissance mechanical imitations of animals, through Decartes’ wind pipe nerves, to present day discussions on the computer and the brain, runs a continuous thread. In fact, the very name of mechanism for an attitude of inquiry throughout the history of Biology reveals this at a philosophical level ([4] and [6]). More often than not, mechanism is mentioned in opposition to vitalism, as an assertion of the validity of the objectivity principle in biology: there are no purposes in animal nature; its apparent purposefulness is similar to the purposefulness of machines. Yet, the fact that one picks machines as a set of objects comparable to living systems, deserves a closer look. What in machines makes it possible to establish such a connection?